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Elsevier

Books in Mathematics

The Mathematics collection presents a range of foundational and advanced research content across applied and discrete mathematics, including fields such as Computational Mathematics; Differential Equations; Linear Algebra; Modelling & Simulation; Numerical Analysis; Probability & Statistics.

  • Delay and Functional Differential Equations and Their Applications

    • 1st Edition
    • Klaus Schmitt
    • English
    Delay and Functional Differential Equations and Their Applications provides information pertinent to the fundamental aspects of functional differential equations and its applications. This book covers a variety of topics, including qualitative and geometric theory, control theory, Volterra equations, numerical methods, the theory of epidemics, problems in physiology, and other areas of applications. Organized into two parts encompassing 25 chapters, this book begins with an overview of problems involving functional differential equations with terminal conditions in function spaces. This text then examines the numerical methods for functional differential equations. Other chapters consider the theory of radiative transfer, which give rise to several interesting functional partial differential equations. This book discusses as well the theory of embedding fields, which studies systems of nonlinear functional differential equations that can be derived from psychological postulates and interpreted as neural networks. The final chapter deals with the usefulness of the flip-flop circuit. This book is a valuable resource for mathematicians.

  • Probabilistic Analysis and Related Topics

    Volume 3
    • 1st Edition
    • A. T. Bharucha-Reid
    • English
    Probabilistic Analysis and Related Topics, Volume 3 focuses on the continuity, integrability, and differentiability of random functions, including operator theory, measure theory, and functional and numerical analysis. The selection first offers information on the qualitative theory of stochastic systems and Langevin equations with multiplicative noise. Discussions focus on phase-space evolution via direct integration, phase-space evolution, linear and nonlinear systems, linearization, and generalizations. The text then ponders on the stability theory of stochastic difference systems and Markov properties for random fields. Topics include Markov property of solutions of stochastic partial differential equations; Markov property for generalized Gaussian random fields; Markov properties for generalized random fields; stochastic stability of nonlinear systems; and linear stochastic systems. The publication examines the method of random contractors and its applications to random nonlinear equations, including integral contractors and applications to random equations; random contractors with random nonlinear majorant functions; and random contractors and application to random nonlinear operator equations. The selection is a valuable reference for mathematicians and researchers interested in the general theory of random functions.

  • Mathematics for Dynamic Modeling

    • 1st Edition
    • Edward Beltrami
    • English
    Mathematics for Dynamic Modeling provides an introduction to the mathematics of dynamical systems. This book presents the mathematical formulations in terms of linear and nonlinear differential equations. Organized into two parts encompassing nine chapters, this book begins with an overview of the notions of equilibrium and stability in differential equation modeling that occur in the guise of simple models in the plane. This text then focuses on nonlinear models in which the limiting behavior of orbits can be more complicated. Other chapters consider the problems that illustrate the concepts of equilibrium and stability, limit cycles, chaos, and bifurcation. This book discusses as well a variety of topics, including cusp catastrophes, strange attractors, and reaction–diffusion and shock phenomena. The final chapter deals with models that are based on the notion of optimization. This book is intended to be suitable for students in upper undergraduate and first-year graduate course in mathematical modeling.

  • Asymptotic Approximations of Integrals

    Computer Science and Scientific Computing
    • 1st Edition
    • R. Wong
    • Werner Rheinboldt + 1 more
    • English
    Asymptotic Approximations of Integrals deals with the methods used in the asymptotic approximation of integrals. Topics covered range from logarithmic singularities and the summability method to the distributional approach and the Mellin transform technique for multiple integrals. Uniform asymptotic expansions via a rational transformation are also discussed, along with double integrals with a curve of stationary points. For completeness, classical methods are examined as well. Comprised of nine chapters, this volume begins with an introduction to the fundamental concepts of asymptotics, followed by a discussion on classical techniques used in the asymptotic evaluation of integrals, including Laplace's method, Mellin transform techniques, and the summability method. Subsequent chapters focus on the elementary theory of distributions; the distributional approach; uniform asymptotic expansions; and integrals which depend on auxiliary parameters in addition to the asymptotic variable. The book concludes by considering double integrals and higher-dimensional integrals. This monograph is intended for graduate students and research workers in mathematics, physics, and engineering.

  • Surveys in Applied Mathematics

    Essays Dedicated to S.M. Ulam
    • 1st Edition
    • N. Metropolis + 2 more
    • English
    Surveys in Applied Mathematics: Essays Dedicated to S.M. Ulam covers the proceedings of the First Los Alamos Symposium on Mathematics in the Natural Sciences. The book focuses on the processes, principles, methodologies, and applications of mathematics in the natural sciences. The selection first offers information on the role of applied mathematics, shape of a curve, and biased versus unbiased estimation. Discussions focus on the James-Stein estimator, automorphic forms and Poincaré series, Poincaré metrics, Schottky space and augmented Schottky space, and Schottky groups and Riemann surfaces. The text then examines algorithms, Whitney numbers of geometric lattices, and continued fraction expansion of algebraic numbers. The book takes a look at bifurcations in reaction-diffusion problems, survey of some finite element methods proposed for treating the Dirichlet problem, and mathematics of quantum fields. Topics include Dirichlet problem, chemical waves and reaction-diffusion equations, and bifurcation theorems. The text then ponders on almost periodic behavior of nonlinear waves, turbulence theory, and renormalization group methods. The selection is a valuable source of information for mathematicians and researchers interested in applied mathematics.

  • Transonic, Shock, and Multidimensional Flows

    Advances in Scientific Computing
    • 1st Edition
    • Richard E. Meyer
    • English
    Mathematics Research Center Symposium: Transonic, Shock, and Multidimensional Flows: Advances in Scientific Computing covers the lectures presented at a Symposium on Transonic, Shock, and Multidimensional Flows, held in Madison on May 13-15, 1981, under the auspices of the Mathematics Research Center of the University of Wisconsin. The book focuses on the advancements in the scientific computation of high-speed aerodynamic phenomena and related fluid motions. The selection first elaborates on computational fluid dynamics of airfoils and wings; shock-free configurations in two- and three-dimensional transonic flow; and steady-state solution of the Euler equations for transonic flow. Discussions focus on boundary conditions, convergence acceleration, indirect design of airfoils, and trailing edge and the boundary layer. The text then examines the calculation of transonic potential flow past three-dimensional configurations and remarks on the numerical solution of Tricomi-type equations. The manuscript ponders on the design and numerical analysis of vortex methods, shock calculations and the numerical solution of singular perturbation problems, tracking of interfaces for fluid flow, and transonic flows with viscous effects. Topics include numerical algorithm, difference approximation for scalar equations, boundary conditions, transonic flow in a tube, and governing equations. The selection is a dependable reference for researchers interested in transonic, shock, and multidimensional flows.

  • Algorithmic Graph Theory and Perfect Graphs

    • 1st Edition
    • Martin Charles Golumbic
    • Werner Rheinboldt
    • English
    Algorithmic Graph Theory and Perfect Graphs provides an introduction to graph theory through practical problems. This book presents the mathematical and algorithmic properties of special classes of perfect graphs. Organized into 12 chapters, this book begins with an overview of the graph theoretic notions and the algorithmic design. This text then examines the complexity analysis of computer algorithm and explains the differences between computability and computational complexity. Other chapters consider the parameters and properties of a perfect graph and explore the class of perfect graphs known as comparability graph or transitively orientable graphs. This book discusses as well the two characterizations of triangulated graphs, one algorithmic and the other graph theoretic. The final chapter deals with the method of performing Gaussian elimination on a sparse matrix wherein an arbitrary choice of pivots may result in the filling of some zero positions with nonzeros. This book is a valuable resource for mathematicians and computer scientists.

  • Weak Convergence of Measures

    Probability and Mathematical Statistics: A Series of Monographs and Textbooks
    • 1st Edition
    • Harald Bergström
    • Z. W. Birnbaum + 1 more
    • English
    Weak Convergence of Measures provides information pertinent to the fundamental aspects of weak convergence in probability theory. This book covers a variety of topics, including random variables, Hilbert spaces, Gaussian transforms, probability spaces, and random variables. Organized into six chapters, this book begins with an overview of elementary fundamental notions, including sets, different classes of sets, different topological spaces, and different classes of functions and measures. This text then provides the connection between functionals and measures by providing a detailed introduction of the abstract integral as a bounded, linear functional. Other chapters consider weak convergence of sequences of measures, such as convergence of sequences of bounded, linear functionals. This book discusses as well the weak convergence in the C- and D-spaces, which is reduced to limit problems. The final chapter deals with weak convergence in separable Hilbert spaces. This book is a valuable resource for mathematicians.

  • Elements of Differentiable Dynamics and Bifurcation Theory

    • 1st Edition
    • David Ruelle
    • English
    Elements of Differentiable Dynamics and Bifurcation Theory provides an introduction to differentiable dynamics, with emphasis on bifurcation theory and hyperbolicity that is essential for the understanding of complicated time evolutions occurring in nature. This book discusses the differentiable dynamics, vector fields, fixed points and periodic orbits, and stable and unstable manifolds. The bifurcations of fixed points of a map and periodic orbits, case of semiflows, and saddle-node and Hopf bifurcation are also elaborated. This text likewise covers the persistence of normally hyperbolic manifolds, hyperbolic sets, homoclinic and heteroclinic intersections, and global bifurcations. This publication is suitable for mathematicians and mathematically inclined students of the natural sciences.

  • Contributions to Correlational Analysis

    • 1st Edition
    • Robert J. Wherry
    • English
    Contributions to Correlational Analysis provides information pertinent to the fundamental aspects of correlational analysis that can be used to replace and enhance many of the parametric and nonparametric inferential statistical tests. This book discusses the basic concern of correctional analysis, which is the relationship between two sets of measure. Organized into 18 chapters, this book begins with an overview of the nature of correction analysis. This text then explains the simple linear relationships in which explains the simple linear relationships in which Y and X each consists of some single measurement per person and the relationship is assumed to be linear. Other chapters consider basic ways of expanding the process to include more or different measurements of either X or Y but with no attempt to find the best functions. This book discusses as well the topic of factor analysis. The final chapter deals with canonical correlation. This book is a valuable resource for psychologists.

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